C₁₉×#1683 #14559540

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1665
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#1683

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#121
commutator, Frattini, cosocle	C₄²	C₂³×C₁₉
prime radical	C₂×D₄×C₁₉	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

160 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,24)(23,25)(26,27)(28,29,32,35)(30,36,39,43)(31,40,37,34)(33,41,42,38);(21,24)(25,26)(28,30,37,41,32,39,31,38)(29,33,40,43,35,42,34,36);(21,25)(23,27)(24,26)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1683, C₁₉×#19110, C₁₉×#19126, …
maximal normal subgroup of	C₂×C₁₉×#1683, C₁₉×#19110, C₁₉×#19126, …
maximal quotient of	C₁₉×#8648, C₁₉×#9215, C₁₉×#9219, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 415);